Geology Reference
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and makes the Boltzmann factor and therefore k
The value of the activation energy tells us how sensi-
tive the rate of a reaction will be to changes in temper-
ature, and measuring this temperature-dependence
provides the means by which E a can be determined
experimentally. (Because it is not a net energy change
between reactants and products like Δ H , E a cannot be
measured calorimetrically.) Transforming both sides of
Equation 3.5 into natural logarithms ('ln' - see
Appendix A), one gets:
Lower temperature
Higher temperature
E x
=− ⋅ +
Energy ( E )
Figure 3.4 Molecular kinetic-energy distribution for two
temperatures. The shaded areas show the portions of each
distribution that lie above a specified energy E x . This
proportion is greater at the higher temperature.
which has a linear form: y = m . x + c (see Appendix A).
Thus if ln k (' y' ) is plotted against 1/ T (' x', T being in
kelvins), a straight line should be observed as shown
in Figure  3.2b and discussed in Appendix A. The
gradient of this line is − E a / R . The numerical value
of  the  activation energy can therefore be established
by  repeating the rate experiment at a number of pre-
determined temperatures, and plotting the rate con-
stants obtained in the form shown in Figure 3.2b. Such
a diagram is called an Arrhenius plot . An Arrhenius plot
for reaction 3.1 is illustrated in Figure 3.5a. A geochem-
ical example is shown in Figure 3.5b. See also Exercise
3.2 at the end of the chapter.
For a collision between reactant molecules to lead to
the formation of product molecules, it must derive suf-
ficient thermal energy from the participants to gener-
ate the activated complex. From theoretical calculations
one can predict the kinetic energy distribution among
reactant molecules at a given temperature T : the results
are illustrated for two alternative temperatures in
Figure 3.4. One can show that the proportion of molec-
ular encounters involving kinetic energies greater than
some critical threshold energy E x (shaded areas in
Figure 3.4) is given by:
Photochemical reactions
Proportion of molecularcollisions
Is a rise in temperature the only mechanism by which
reactant molecules can surmount the activation energy
barrier? A number of gas reactions known to take place
in the stratosphere show that energetic photons from
the Sun provide an alternative means of energizing
molecules into reacting. One example is the formation
of stratospheric ozone (O 3 ):
− /
The term on the right is called the Boltzmann factor . It
appears in the Arrhenius equation as a measure of the
proportion of the reactant molecule collisions that pos-
sess sufficient energy (i.e. greater than E a ) at the tem-
perature T to reach the transition state and thereby to
complete the reaction. The form of the Boltzmann fac-
tor shows that an increase of temperature will shift
the  energy distribution towards higher energies
(Figure  3.4), so that a greater proportion of reactant
molecules can collide with energies exceeding E a and
surmount the energy hurdle, like water flowing over a
weir. In other words the reaction rate will increase. But
reducing the temperature will inhibit the reaction,
because − E a / RT becomes a larger negative number
The intense flux of solar ultraviolet (UV) radiation -
see Box 6.3 - in the upper atmosphere causes a small
proportion of oxygen molecules to disintegrate into
separate oxygen atoms which, by virtue of their dis-
rupted chemical bonds (represented by the symbol
O •),are highly reactive: they effectively sit on top of the
energy barrier shown in Figure 3.3. Collision of either
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